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Abstract In this paper, we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations. After revisiting earlier continuum approximations, we propose a regularized continuum model variant to approximate the discrete granular crystal model through a suitable partial differential equation. We then compute, both analytically and numerically, its travelling wave and periodic travelling wave solutions, in addition to its conservation laws. Next, using the periodic solutions, we describe quantitatively various features of the dispersive shock wave (DSW) by applying Whitham modulation theory and the DSW fitting method. Finally, we perform several sets of systematic numerical simulations to compare the corresponding DSW results with the theoretical predictions and illustrate that the continuum model provides a good approximation of the underlying discrete one. 

IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments. MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically. Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available. 

The discovery of cell penetrating peptides (CPPs) with unique membrane activity has inspired the design and synthesis of a variety of cell penetrating macromolecules, which offer tremendous opportunity and promise for intracellular delivery of a variety of imaging probes and therapeutics. While cell penetrating macromolecules can be designed and synthesized to have equivalent or even superior cell penetrating activity compared with natural CPPs, most of them suffer from moderate to severe cytotoxicity. Inspired by recent advances in peptide self-assembly and cell penetrating macromolecules, in this work, we demonstrated a new class of peptide assemblies with intrinsic cell penetrating activity and excellent cytocompatibility. Supramolecular assemblies were formed through the self-assembly of de novo designed multidomain peptides (MDPs) with a general sequence of K x (QW) 6 E y in which the numbers of lysine and glutamic acid can be varied to control supramolecular assembly, morphology and cell penetrating activity. Both supramolecular spherical particles and nanofibers exhibit much higher cell penetrating activity than monomeric MDPs while supramolecular nanofibers were found to further enhance the cell penetrating activity of MDPs. In vitro cell uptake results suggested that the supramolecular cell penetrating nanofibers undergo macropinocytosis-mediated internalization and they are capable of escaping from the lysosome to reach the cytoplasm, which highlights their great potential as highly effective intracellular therapeutic delivery vehicles and imaging probes. 

As sessile organisms, plants have evolved unique patterns of growth and development, elaborate metabolism and special perception and signaling mechanisms to environmental cues. Likewise, plants have complex and highly special programs for transcriptional control of gene expression. A case study for the special transcription control in plants is the expansion of general transcription factors, particularly the family of Transcription Factor IIB (TFIIB)-like factors with 15 members in Arabidopsis. For more than a decade, molecular and genetic analysis has revealed important functions of these TFIIB-like factors in specific biological processes including gametogenesis, pollen tube growth guidance, embryogenesis, endosperm development, and plant-microbe interactions. The redundant, specialized, and diversified roles of these TFIIB-like factors challenge the traditional definition of general transcription factors established in other eukaryotes. In this review, we discuss general transcription factors in plants with a focus on the expansion and functional analysis of plant TFIIB-like proteins to highlight unique aspects of plant transcription programs that can be highly valuable for understanding the molecular basis of plant growth, development and responses to stress conditions. 

Supramolecular assembly and PEGylation (attachment of a polyethylene glycol polymer chain) of peptides can be an effective strategy to develop antimicrobial peptides with increased stability, antimicrobial efficacy and hemocompatibility. However, how the self-assembly properties and PEGylation affect their lipid membrane interaction is still an unanswered question. In this work, we use state-of-the-art small angle X-ray and neutron scattering (SAXS/SANS) together with neutron reflectometry (NR) to study the membrane interaction of a series of multidomain peptides, with and without PEGylation, known to self-assemble into nanofibers. Our approach allows us to study both how the structure of the peptide and the membrane are affected by the peptide–lipid interactions. When comparing self-assembled peptides with monomeric peptides that are not able to undergo assembly due to shorter chain length, we found that the nanofibers interact more strongly with the membrane. They were found to insert into the core of the membrane as well as to absorb as intact fibres on the surface. Based on the presented results, PEGylation of the multidomain peptides leads to a slight net decrease in the membrane interaction, while the distribution of the peptide at the interface is similar to the non-PEGylated peptides. Based on the structural information, we showed that nanofibers were partially disrupted upon interaction with phospholipid membranes. This is in contrast with the considerable physical stability of the peptide in solution, which is desirable for an extended in vivo circulation time. 

A self-assembling peptide nanofiber was developed to sense the microenvironmental pH change associated with bacterial growth. Using a near-infrared probe, a strong correlation was observed between the local pH reduction of bacterial colonies with the degree of peptide disassembly, which led to their enhanced antimicrobial activity against anaerobic bacteria. 

This work demonstrates a modular design strategy based on the supramolecular assembly of multidomain peptides to fabricate reduction-responsive cell penetrating nanofibers (CPNs), which hold great promise for selective targeting of cancer therapeutics to tumor cells.